What types of Hypotheses are there?
- The statistical hypotheses are set up as two options (H0 and H1), but H1 is also known as HA
What is the difference between (H0 and H1) of a Hypotheses?
- H0 and H1 have to cover every possibility
- The Null Hypothesis (Ho) has to state that nothing has happened- the status quo - this is what we will accept unless the data shows otherwise
- The Alternative Hypothesis (H1 or HA) has to cover everything else
What are some characteristics of the Null hypotheses?
- It is always the hypothesis that we want to disprove
- It is usually opposite to what the researcher wants to prove
- It is stated in terms of population parameters
What types of tests can we have when setting up a hypotheses?
- One or two tailed tests
What is two tailed testing?
Two tailed testing: Non directional hypothesis
- H0: the means are equal
- H1: the means are not equal
What is one tailed testing?
One tailed testing: Directional hypotheses
- H0: Nothing changed
- H1: Less or greater than
Study the example of Two Tailed Testing
- If we are interested in the effect of two different soils on the growth rate of plants
- Hypotheses (English): the H0 is that there is no difference in the population mean growth rate of plants
- The H1 will state that there was a difference
- Hypotheses (Symbols):
H0: μ = μ
H1: μ does not = μ
Study the Example of One Tailed Testing
- Is the NOX in the atmosphere increasing from time 1 to time 2?
- Hypotheses (English): H0: The population NOX levels either stayed the same or decreased from time 1 to time 2 (ie: they did not increase). H1: The NOX levels increased from time 1 to time 2
- Hypotheses (Symbols):
H0: μ1 > μ2
H1: μ1 < μ2
What is a decision rule?
- A formal rule that states, based on the data obtained, when to reject the null hypothesis H0
What is a test statistic?
- A statistic used in statistical hypothesis testing
What does the Decision Rule depend on?
- Depending on where our Test statistic (which we will be calculating later) falls within the sampling distribution, we will be rejecting or accepting H0
What are the seven components of a hypotheses test?
- H0 (What the researcher is investigating)
- H1 or HA (Alternate Hypotheses; your research question; what you are trying to show)
- α (significance level; when do we reject the null hypotheses
- dR (Decision Rule; Where we use the α to get the value for our decision)
- ts (Test Statistic; is a formula)
- tsv (Test statistic value; point estimate; another formula)
- con (Conclusion; where we take the tsv and compare it to our decision rule
What is a hypotheses test?
Question and ask whether we have the evidence to suggest something has changed or something is different
What does it mean when the null hypotheses is rejected?
- This means that the Null Hypotheses is no longer correct
What are the two different types of one sample tests?
- One sample z test
- One sample t test
How do you know which one sample test to use?
There is a rule in statistics that states:
- Whenever you have σ you always use the z test
- Whenever you have S you always use the t test
What does every test in statistics have?
- Assumptions
- In every part of statistics there is some level of unknown that should be there so that the data can be numerical
What are some examples of assumptions for z tests?
- Underlying population distribution is a Normal distribution
- Samples are independent and random observations
What is assumed about the model in z tests?
- Every sample observation can be modelled
- The model consists of a determined (explained) component and a random (unexplained) component
- Each obs. = grand mean + sample effect + random
variation
What can a “one sample t test” test?
- If the population mean is equal to a set value: Two tailed test.
- If the population mean is greater (or smaller) than a set value: One tailed test
What are some assumptions that need to be made for a t test?
- The observations in the sample should be random and independent (sampled without bias).
- The population distribution is a Normal distribution - the test is reasonably robust to departures from this assumption
What happens to the t test if n is larger than 30?
- If n, and therefore df, is large (> 30) then a Normal distribution can be used instead of a t-distribution
Study the process for finding the test statistic in a t test
https://docs.google.com/document/d/1r_ttbYs-4jXdkBbVGPH9vk1swjRRmRJUWdllcJXdaAI/edit?usp=sharing
What should a t Test conclusion have?
- You should always state the conclusion in plain English (no statistical jargon).
- You should state the probability associated with your conclusion.
- Example - For a two tailed test: The DO in the stream was significantly (p < 0.05 or
p = 0.002) different than 3. - Example - For a one tailed test: The species richness for the rain forest site is not significantly (p > 0.05 or p = 0.210) higher than 150
